Question: Graph this system of equations and solve. $14x-4y = 20$ $-x+2y = 2$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Answer: Convert the first equation, $14x-4y = 20$ , to slope-intercept form. $y = \dfrac{7}{2} x - 5$ The y-intercept for the first equation is $-5$ , so the first line must pass through the point $(0, -5)$ The slope for the first equation is $\dfrac{7}{2}$ . Remember that the slope tells you rise over run. So in this case for every $7$ positions you move up You must also move $2$ positions to the right. $2$ positions to the right. $7$ positions up from $(0, -5)$ is $(2, 2)$ Graph the blue line so it passes through $(0, -5)$ and $(2, 2)$ Convert the second equation, $-x+2y = 2$ , to slope-intercept form. $y = \dfrac{1}{2} x + 1$ The y-intercept for the second equation is $1$ , so the second line must pass through the point $(0, 1)$ The slope for the second equation is $\dfrac{1}{2}$ . Remember that the slope tells you rise over run. So in this case for every $1$ position you move up You must also move $2$ positions to the right. $2$ positions to the right. Graph the green line so it passes through $(0, 1)$ and $(2, 2)$ The solution is the point where the two lines intersect. The lines intersect at $(2, 2)$.